Resonant and non-resonant beat-wave excitation of relativistic plasma waves

The phase relationship between a beat-wave excited relativistic plasma wave and its laser pulse driver is important for the phase-locked acceleration of externally injected electrons. This relationship is studied using 2-D particle-in-cell simulations for both the resonant and non-resonant waves excited in a non-uniform plasma whose density is a time and space-varying quantity due to the slow ponderomotive expulsion of the plasma electrons by the laser pulse. It is found that the waves excited at the resonant density get dephased with respect to the beat pattern of the laser pulse. Therefore, externally injected electrons could interact with both accelerating and decelerating fields of the plasma wave, resulting in a decrease in the overall energy gain. Furthermore, the dynamics of this dephasing is highly sensitive of the initial plasma density and laser pulse parameters, as it is expected from an oscillator being driven just slightly off resonance. As opposed to the resonant case, the accelerating electric fields associated with the extremely non-resonant plasmons are always in phase with the beat-pattern of the laser pulse, regardless of the variations in the plasma density. Although the normalized amplitude of the oscillation is small, the longitudinal electric field of such a wave can still be substantial if the plasma density is much higher than the resonant density. The excitation of such non-resonant relativistic plasma waves by a TW CO₂ laser pulse is shown to be possible for plasma densities as high as 12 times the resonant density. The density fluctuations and the fields associated with these waves are measured experimentally with a novel collinear Thomson scattering diagnostic system and by the energy change of the injected electrons, respectively.